Correction on ‘Population Genetics Models with Skewed Fertilities: A Forward and Backward Analysis’

Abstract

The article ’Population genetics models with skewed fertilities: a forward and backward analysis’, Stochastic Models 27, 521–554 (2011) contains at the top of page 536 a formula for the joint factorial moments of the offspring numbers μ1,…, μ N , which is wrong in that generality. The only compound Poisson models for which this formula holds true are skewed generalized Wright–Fisher models and skewed generalized Dirichlet models. In this note we correct the erroneous results in Section 4 of the mentioned article from Proposition 4.2 on. The main conclusion that many symmetric compound Poisson population models are in the domain of attraction of the Kingman coalescent, remains valid. However, the proofs turn out to be more involved and the time-scaling differs from the erroneous time-scaling provided in the original article.